At the risk of sounding glib, I’ve always maintained that if you want to run faster, you need to run faster. Likewise, if you want to get better at running hills, you have to run hills.
Incorporating hills into your training runs will help you develop both strength and speed. The muscles around your knees will get stronger, lessening the risk of knee injuries, and your stride will become more efficient on account of your overall leg and core strength.
Hills, like big waves, need to be approached with care and respect. Be particularly vigilant if you are prone to knee or calf injury, or Achilles tendonitis.
We are very lucky in Maine because it is relatively easy to incorporate hills into our runs. If you are not familiar with running on hills, I recommend you find something gradual and not too long, with a “backside” to practice running downhill too (more on that in a minute). If you can, plot a course that includes a few hills. I am not advocating doing hill “repeats” at this time, simply varying your running terrain to include some up and down.
As you approach the hill, pick up your pace slightly without changing the rhythm of your run. Remember that the idea of hill work is to negotiate the hills efficiently, with as little disruption as possible to your rhythm. Think of yourself rolling over the hill, almost as if it isn't there. Concentrate on keeping your upper body relaxed, while you let your legs do the work. Positive affirmations and visualizations are hugely helpful tools for running uphill. My favorites are "I love hills!" and "Hills are my friends."
On gradual inclines, try to run a bit harder than you had been running on the flat before the hill. On steeper inclines, concentrate on lifting your knees and pushing off hard with every step. This attention to your "vertical" motion is at least as important as your forward motion up the hill. The steeper the hill, the more you should lift your knees. On the steepest inclines try to lift your knees so high that your thighs reach horizontal. I think of stepping up a set of stairs. Using your arm strength helps, too.
Even for very long hills (a mile or longer), try to maintain the exaggerated knee lifts. The benefits will make themselves known soon enough. The knee lifts are not easy. But even with the extra workout, your legs take less of a pounding running uphill than when running hard on the flat or downhills - you're not hitting the ground as hard.
As you reach the top of each hill, focus on running all the way over the top until your reach the flat, and resume your regular running rhythm again.
Downhill running also requires technique and practice, and if done well, can be extremely strategic in a race situation. Many people lean back and put their brakes on while descending a hill. Think about alpine skiing…you lean forward and open yourself up to the descent. You will fly by your competition.
Over the years, while running downhill, I’ve practiced opening up my hips, leaning (not bending at the waist) forward, maintaining strong arms and good control, and paying very close attention to my footfall. Think quick feet, hitting the ground as lightly as possible without over-striding. Maintain good control of your stride while increasing your turnover. Remember, you’ve got gravity working for you. Focus on good, relaxed running form, and enjoy the ride!